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-   -   Lee-Carter Model (http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=336824)

 koudai8 12-06-2018 04:32 PM

Lee-Carter Model

The phrase "stochastic model" brings to mind models whose output are random. For example, the Cox-Ingersoll-Ross interest rate model, where outputs depend on a random error term.

For Lee-Carter model, I can't quite wrap my head around why it's considered "stochastic". To me, it seems once the parameters are properly calibrated with past data, the projection of future mortality rates are deterministic--ln(mu_xt) = alpha_x + beta_x * kappa_t.

So why is this classified as stochastic?

My thoughts: is it because in the framework, we assumed that there is an error term, although we're not actually projecting it? Or is it because kappa_t is a variable indexed by time?

Thanks.

 Jim Daniel 12-06-2018 09:07 PM

Quote:
 Originally Posted by koudai8 (Post 9492259) The phrase "stochastic model" brings to mind models whose output are random. For example, the Cox-Ingersoll-Ross interest rate model, where outputs depend on a random error term. For Lee-Carter model, I can't quite wrap my head around why it's considered "stochastic". To me, it seems once the parameters are properly calibrated with past data, the projection of future mortality rates are deterministic--ln(mu_xt) = alpha_x + beta_x * kappa_t. So why is this classified as stochastic? My thoughts: is it because in the framework, we assumed that there is an error term, although we're not actually projecting it? Or is it because kappa_t is a variable indexed by time? Thanks.
It's because K_t is a Normal random variable.

 cyitwei 12-07-2018 01:24 AM

Quote:
 Originally Posted by koudai8 (Post 9492259) The phrase "stochastic model" brings to mind models whose output are random. For example, the Cox-Ingersoll-Ross interest rate model, where outputs depend on a random error term. For Lee-Carter model, I can't quite wrap my head around why it's considered "stochastic". To me, it seems once the parameters are properly calibrated with past data, the projection of future mortality rates are deterministic--ln(mu_xt) = alpha_x + beta_x * kappa_t. So why is this classified as stochastic? My thoughts: is it because in the framework, we assumed that there is an error term, although we're not actually projecting it? Or is it because kappa_t is a variable indexed by time? Thanks.

The K_t is a functional of Normal distrn.

If you look close enough, it's a random walk with a constant drift, or a AR(1) process in time series.

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